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Dzongkha Numerals
Dzongkha, the national language of Bhutan, has two numeral systems, one vigesimal (base 20), and a modern decimal system. The vigesimal system remains in robust use. Ten is an auxiliary base: the -teens are formed with ten and the numerals 1–9. Vigesimal[edit]1 ciː 11 cu-ci2 ˈɲiː 12 cu-ɲi3 sum 13 cu-sum4 ʑi 14 cu-ʑi5 ˈŋa 15 ce-ŋa6 ɖʱuː 16 cu-ɖu7 dyn 17 cup-dỹ8 ɡeː 18 cop-ɡe9 ɡuː 19 cy-ɡu10 cu-tʰãm* 20 kʰe ciː*When it appears on its own, 'ten' is usually said cu-tʰãm 'a full ten'. In combinations it is simply cu. Factors of 20 are formed from kʰe. Intermediate factors of ten are formed with pɟʱe-da 'half to':30 kʰe pɟʱe-da ˈɲiː (a half to two score)40 kʰe ˈɲiː (two score)50 kʰe pɟʱe-da sum (a half to three score)100 kʰe ˈŋa (five score)200 kʰe cutʰãm (ten score)300 kʰe ceŋa (fifteen score)400 (20²) ɲiɕu is the next unit: ɲiɕu ciː 400, ɲiɕu ɲi 800, etc
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Numeral System
A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. It can be seen as the context that allows the symbols "11" to be interpreted as the binary symbol for three, the decimal symbol for eleven, or a symbol for other numbers in different bases. The number the numeral represents is called its value. Ideally, a numeral system will:Represent a useful set of numbers (e.g. all integers, or rational numbers) Give every number represented a unique representation (or at least a standard representation) Reflect the algebraic and arithmetic structure of the numbers.For example, the usual decimal representation of whole numbers gives every nonzero whole number a unique representation as a finite sequence of digits, beginning with a non-zero digit
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Kaktovik Inupiaq Numerals
Inuit, like other Eskimo languages (and Celtic and Mayan languages as well), uses a vigesimal counting system. Inuit counting has sub-bases at 5, 10, and 15. Arabic numerals, consisting of 10 distinct digits (0-9) are not adequate to represent a base-20 system. Students from Kaktovik, Alaska, came up with the Kaktovik Inupiaq numerals,[1] which has since gained wide use among Alaskan Iñupiaq, and is slowly gaining ground in other countries where dialects of the Inuit language are spoken.[2] The numeral system has helped to revive counting in Inuit, which had been falling into disuse among Inuit speakers due to the prevalence of the base-10 system in schools. The picture below shows the numerals 1–19 and then 0
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Greek Numerals
Greek numerals, also known as Ionic, Ionian, Milesian, or Alexandrian numerals, are a system of writing numbers using the letters of the Greek alphabet. In modern Greece, they are still used for ordinal numbers and in contexts similar to those in which Roman numerals
Roman numerals
are still used elsewhere in the West. For ordinary cardinal numbers, however, Greece
Greece
uses Arabic numerals.Contents1 History 2 Description 3 Table 4 Higher numbers 5 Zero 6 See also 7 References 8 External linksHistory[edit] The Minoan and Mycenaean civilizations' Linear A
Linear A
and Linear B alphabets used a different system, called Aegean numerals, which included specialized symbols for numbers: 𐄇 = 1, 𐄐 = 10, 𐄙 = 100, 𐄢 = 1000, and 𐄫 = 10000.[1] Attic numerals, which were later adopted as the basis for Roman numerals, were the first alphabetic set
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Hebrew Numerals
The system of Hebrew numerals
Hebrew numerals
is a quasi-decimal alphabetic numeral system using the letters of the Hebrew alphabet. The system was adapted from that of the Greek numerals
Greek numerals
in the late 2nd century BC. The current numeral system is also known as the Hebrew alphabetic numerals to contrast with earlier systems of writing numerals used in classical antiquity. These systems were inherited from usage in the Aramaic and Phoenician scripts, attested from c. 800 BC in the so-called Samaria ostraca
Samaria ostraca
and sometimes known as Hebrew-Aramaic numerals, ultimately derived from the Egyptian Hieratic numerals. The Greek system was adopted in Hellenistic Judaism
Hellenistic Judaism
and had been in use in Greece since about the 5th century BC. [1] In this system, there is no notation for zero, and the numeric values for individual letters are added together
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Roman Numerals
The numeric system represented by Roman numerals
Roman numerals
originated in ancient Rome
Rome
and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers in this system are represented by combinations of letters from the Latin
Latin
alphabet. Roman numerals, as used today, are based on seven symbols:[1]Symbol I V X L C D MValue 1 5 10 50 100 500 1,000The use of Roman numerals
Roman numerals
continued long after the decline of the Roman Empire
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Aegean Numerals
Aegean numbers was the numeral system used by the Minoan and Mycenaean civilizations.[1] They are attested in Linear A
Linear A
and Linear B
Linear B
scripts. They may have survived in the Cypro-Minoan script, where a single sign with "100" value is attested so far on a large
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Attic Numerals
Attic numerals
Attic numerals
were used by the ancient Greeks, possibly from the 7th century BC. They were also known as Herodianic numerals because they were first described in a 2nd-century manuscript by Herodian. They are also known as acrophonic numerals because the symbols derive from the first letters of the words that the symbols represent: five, ten, hundred, thousand and ten thousand. See Greek numerals
Greek numerals
and acrophony.Decimal Symbol Greek numeral IPA1 Ι – –5 Π πέντε [pɛntɛ]10 Δ δέκα [deka]100 Η ἑκατόν [hɛkaton]1000 Χ χίλιοι / χιλιάς [kʰilioi / kʰilias]10000 Μ μύριον [myrion]The use of Η for 100 reflects the early date of this numbering system: Η (Eta) in the early Attic alphabet represented the sound /h/
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Babylonian Numerals
Babylonian numerals
Babylonian numerals
were written in cuneiform, using a wedge-tipped reed stylus to make a mark on a soft clay tablet which would be exposed in the sun to harden to create a permanent record. The Babylonians, who were famous for their astronomical observations and calculations (aided by their invention of the abacus), used a sexagesimal (base-60) positional numeral system inherited from either the Sumerian or the Eblaite civilizations.[1] Neither of the predecessors was a positional system (having a convention for which ‘end’ of the numeral represented the units).Contents1 Origin 2
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Brahmi Numerals
The Brahmi numerals
Brahmi numerals
are a numeral system attested from the 3rd century BCE (somewhat later in the case of most of the tens). They are the direct graphic ancestors of the modern Indian and Hindu–Arabic numerals. However, they were conceptually distinct from these later systems, as they were not used as a positional system with a zero. Rather, there were separate numerals for each of the tens (10, 20, 30, etc.). There were also symbols for 100 and 1000 which were combined in ligatures with the units to signify 200, 300, 2000, 3000, etc. Origins[edit] The source of the first three numerals seems clear: they are collections of 1, 2, and 3 strokes, in Ashoka's era vertical I, II, III like Roman numerals, but soon becoming horizontal like the modern Chinese numerals. In the oldest inscriptions, 4 is a +, reminiscent of the X of neighboring Kharoṣṭhī, and perhaps a representation of 4 lines or 4 directions
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Chuvash Numerals
Chuvash numerals
Chuvash numerals
is an ancient numeral system from the Old Turkic script the Chuvash people
Chuvash people
used. (Modern Chuvash use Hindu-Arabic numerals.) Those numerals originate from finger numeration. They look like Roman numerals, but larger numerals stay at the right side. It was possible to carve those numerals on wood. In some cases numerals were preserved until the beginning of the 20th century.[1][2]Numeral Chuvash numeral1 I5 /10 X50 (upside down) 𐠂100 𐠀500 𐠁1000 ✳Examples[edit]Hindu-Arabic Chuvash2 II4 IIII6 I/19 IIII/X32 IIXXX47 II/XXXXReferences[edit]^ сентября», Федотова Людмила Аркадьевна, Флегентова Апполинария Алексеевна, Издательский дом «Первое. "Интегрированный урок на тему "Чувашские числовые знаки"
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Egyptian Numerals
The system of ancient Egyptian numerals
Egyptian numerals
was used in Ancient Egypt
Ancient Egypt
from around 3000 BC[1] until the early first millennium AD. It was a system of numeration based on multiples of ten, often rounded off to the higher power, written in hieroglyphs
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Etruscan Numerals
The Etruscan numerals
Etruscan numerals
were used by the ancient Etruscans. The system was adapted from the Greek Attic numerals
Attic numerals
and formed the inspiration for the later Roman numerals
Roman numerals
via the Old Italic script.Etruscan Arabic Symbol * Old Italicθu 1𐌠maχ 5𐌡śar 10𐌢muvalχ 50𐌣? 100 or C 𐌟There is very little surviving evidence of these numerals. Examples are known of the symbols for larger numbers, but it is unknown which symbol represents which number. Thanks to the numbers written out on the Tuscania
Tuscania
dice, there is agreement that zal, ci, huθ and śa are the numbers up to six (besides 1 and 5). The assignment depends on whether the numbers on opposite faces of Etruscan dice add up to seven, like nowadays
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Kharosthi Numerals
Egyptian hieroglyphs
Egyptian hieroglyphs
32 c. BCE Hieratic
Hieratic
32 c. BCEDemotic 7 c. BCEMeroitic 3 c. BCEProto-Sinaitic 19 c. BCEUgaritic 15 c. BCE Epigraphic South Arabian 9 c. BCEGe’ez 5–6 c. BCEPhoenician 12 c. BCEPaleo-Hebrew 10 c. BCESamaritan 6 c. BCE Libyco-Berber
Libyco-Berber
3 c. BCETifinaghPaleohispanic (semi-syllabic) 7 c. BCE Aramaic 8 c. BCE Kharoṣṭhī
Kharoṣṭhī
4 c. BCE Brāhmī 4 c. BCE Brahmic family
Brahmic family
(see)E.g. Tibetan 7 c. CE Devanagari
Devanagari
13 c. CECanadian syllabics 1840Hebrew 3 c. BCE Pahlavi 3 c. BCEAvestan 4 c. CEPalmyrene 2 c. BCE Syriac 2 c. BCENabataean 2 c. BCEArabic 4 c. CEN'Ko 1949 CESogdian 2 c. BCEOrkhon (old Turkic) 6 c. CEOld Hungarian c. 650 CEOld UyghurMongolian 1204 CEMandaic 2 c. CEGreek 8 c. BCEEtruscan 8 c. BCELatin 7 c
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Cyrillic Numerals
Cyrillic numerals
Cyrillic numerals
are a numeral system derived from the Cyrillic script, developed in the First Bulgarian Empire
First Bulgarian Empire
in the late 10th century
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Maya Numerals
The Mayan numeral system was the system to represent numbers and calendar dates in the Maya civilization. It was a vigesimal (base-20) positional numeral system. The numerals are made up of three symbols; zero (shell shape, with the plastron uppermost), one (a dot) and five (a bar). For example, thirteen is written as three dots in a horizontal row above two horizontal bars; sometimes it is also written as three vertical dots to the left of two vertical bars. With these three symbols each of the twenty vigesimal digits could be written.400s20s1s33 429 5125Numbers after 19 were written vertically in powers of twenty. The Mayan used powers of twenty, just as our Hindu-Arabic numeral system uses powers of tens.[1] For example, thirty-three would be written as one dot, above three dots atop two bars. The first dot represents "one twenty" or "1×20", which is added to three dots and two bars, or thirteen. Therefore, (1×20) + 13 = 33
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